Assistant Professor, Mathematics, School of Engineering, Coimbatore

Qualification:

Ph.D, MPhil, MSc

Email:

j_geetha@cb.amrita.edu

Dr. Geetha J. currently serves as Assistant Professor (Sr. Gr.) at the department of Mathematics, School of Engineering, Coimbatore Campus. Her research interests include Graph Theory and Linear Algebra. Geetha has completed M. Sc and M. Phil in Mathematics.

**Project Title: Total coloring conjecture for certain classes of graphs****Role:**CO-PI**Duration:**2014-2016**Funding Agency:**National Board for Higher Mathematics (NBHM)**Project Title: Behzad-Vizing Conjecture on Graph Coloring for Product Graphs****Role:**CO-PI**Duration:**2015-2018**Funding Agency:**Department of Science & Technology - DST**Project Title: Total Colorings for Certain Classes of Cayley Graphs****Role:**PI**Funding Agency:**DST-SERB

Year of Publication | Title |
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2021 |
C. Gopika, J. Geetha, and Dr. Somasundaram K., “Weighted PI index of tensor product and strong product of graphs”, Discrete Mathematics, Algorithms and Applications, vol. 13, p. 2150019, 2021.[Abstract] The Weighted Padmakar–Ivan (PI) index of a connected, simple graph G is given by PIw(G) =∑e=(u,v)∈E(G)((dG(u) + dG(v))(|V (G)|− NG(e))), where NG(e) denotes the number of equidistant vertices of the edge e. In this paper, weighted PI index of tensor product and strong product of some graphs are obtained. More »» |

2021 |
T. P. Sandhiya, J. Geetha, and Dr. Somasundaram K., “Total colorings of certain classes of lexicographic product graphs”, Discrete Mathematics, Algorithms and Applications, p. 2150129, 2021.[Abstract] A total coloring of a graph G is an assignment of colors to all the elements (vertices and edges) of the graph in such a way that no two adjacent or incident elements receive the same color. The Total Chromatic Number, χ″(G) is the minimum number of colors which need to be assigned to obtain a total coloring of the graph G. The Total Coloring Conjecture made independently by Behzad and Vizing claims that, Δ(G) + 1 ≤ χ″(G) ≤ Δ(G) + 2, where Δ(G) represents the maximum degree of G. The lower bound is sharp, the upper bound remains to be proved. In this paper, we prove the Total Coloring Conjecture for certain classes of lexicographic product and deleted lexicographic product of graphs. More »» |

2020 |
R. Vignesh, Mohan, S., J. Geetha, and Dr. Somasundaram K., “Total colorings of core-satellite, cocktail party and modular product graphs”, TWMS Journal of Applied and Engineering Mathematic, vol. 10, no. 3, pp. 778-787, 2020.[Abstract] A total coloring of a graph G is a combination of vertex and edge colorings of G. In other words, is an assignment of colors to the elements of the graph G such that no two adjacent elements (vertices and edges) receive a same color. The total chromatic number of a graph G, denoted by χ00(G), is the minimum number of colors that suffice in a total coloring. Total coloring conjecture (TCC) was proposed independently by Behzad and Vizing that for any graph G, ∆(G) + 1 ≤ χ00(G) ≤ ∆(G) + 2, where ∆(G) is the maximum degree of G. In this paper, we prove TCC for Core Satellite graph, Cocktail Party graph, Modular product of paths and Shrikhande graph. More »» |

2020 |
J. Geetha, Dr. Somasundaram K., and Hung-Lin Fu, “Total colorings of circulant graphs”, Discrete Mathematics, Algorithms and Applications, p. 2150050, 2020.[Abstract] The total chromatic number χ″(G) is the least number of colors needed to color the vertices and edges of a graph G such that no incident or adjacent elements (vertices or edges) receive the same color. Behzad and Vizing proposed a well-known total coloring conjecture (TCC): χ″(G) ≤ Δ(G) + 2, where Δ(G) is the maximum degree of G. For the powers of cycles, Campos and de Mello proposed the following conjecture: Let G = Cnk denote the graphs of powers of cycles of order n and length k with 2 ≤ k < ⌊n 2 ⌋. Then, χ″(G) = Δ(G) + 2, if k > n 3 − 1 and n is odd; and Δ(G) + 1, otherwise. In this paper, we prove the Campos and de Mello’s conjecture for some classes of powers of cycles. Also, we prove the TCC for complement of powers of cycles. More »» |

2020 |
S. Mohan, J. Geetha, and Dr. Somasundaram K., “Total coloring of quasi-line graphs and inflated graphs”, Discrete Mathematics, Algorithms and Applications, vol. 2150060, p. 2150060, 2020.[Abstract] A total coloring of a graph is an assignment of colors to all the elements (vertices and edges) of the graph such that no two adjacent or incident elements receive the same color. A claw-free graph is a graph that does not have K1,3 as an induced subgraph. Quasi-line and inflated graphs are two well-known classes of claw-free graphs. In this paper, we prove that the quasi-line and inflated graphs are totally colorable. In particular, we prove the tight bound of the total chromatic number of some classes of quasi-line graphs and inflated graphs. More »» |

2019 |
R. Vignesh, J. Geetha, and Dr. Somasundaram K., “Total coloring conjecture for vertex, edge and neighborhood corona products of graphs”, Discrete Mathematics, Algorithms and Applications, vol. 11, p. 1950014, 2019.[Abstract] A total coloring of a graph G is an assignment of colors to the elements of the graph G such that no adjacent vertices and edges receive the same color. The total chromatic number of a graph G, denoted by χ″(G), is the minimum number of colors that suffice in a total coloring. Behzad and Vizing conjectured that for any simple graph G, Δ(G) + 1 ≤ χ″(G) ≤ Δ(G) + 2, where Δ(G) is the maximum degree of G. In this paper, we prove the tight bound of the total coloring conjecture for the three types of corona products (vertex, edge and neighborhood) of graphs. More »» |

2018 |
R Vignesh, J. Geetha, and Dr. Somasundaram K., “Total Coloring Conjecture for Certain Classes of Graphs”, Algorithms, vol. 11, p. 161, 2018.[Abstract] A total coloring of a graph G is an assignment of colors to the elements of the graph G such that no two adjacent or incident elements receive the same color. The total chromatic number of a graph G, denoted by , is the minimum number of colors that suffice in a total coloring. Behzad and Vizing conjectured that for any graph G, , where is the maximum degree of G. In this paper, we prove the total coloring conjecture for certain classes of graphs of deleted lexicographic product, line graph and double graph. More »» |

2018 |
J. Geetha and Dr. Somasundaram K., “Total Colorings of Product Graphs”, Graphs and Combinatorics (2018), vol. 34, no. 2, pp. 339–347, 2018.[Abstract] A total coloring of a graph is an assignment of colors to all the elements of the graph in such a way that no two adjacent or incident elements receive the same color. In this paper, we prove Behzad–Vizing conjecture for product graphs. In particular, we obtain the tight bound for certain classes of graphs. More »» |

2017 |
S. Mohan, J. Geetha, and Dr. Somasundaram K., “Total coloring of the corona product of two graphs”, AUSTRALASIAN JOURNAL OF COMBINATORICS, vol. 68, no. 1, pp. 15–22, 2017.[Abstract] A total coloring of a graph is an assignment of colors to all the elements (vertices and edges) of the graph such that no two adjacent or incident elements receive the same color. In this paper, we prove the tight bound of the Behzad and Vizing conjecture on total coloring for the corona product of two graphs G and H, when H is a cycle, a complete graph or a bipartite graph. More »» |

2016 |
S. Mohan, J. Geetha, and Dr. Somasundaram K., “Total Coloring of Certain Classes of Product Graphs”, Electronic Notes in Discrete Mathematics, vol. 53, pp. 173 - 180, 2016.[Abstract] Abstract A total coloring of a graph is an assignment of colors to all the elements of the graph such that no two adjacent or incident elements receive the same color. In this paper, we prove the tight bound of Behzad and Vizing conjecture on total coloring for Compound graph of G and H, where G and H are any graphs. More »» |

2016 |
J. Geetha and Dr. Somasundaram K., “Total Chromatic Number and Some Topological Indices”, Electronic Notes in Discrete Mathematics, vol. 53, pp. 363 - 371, 2016.[Abstract] Abstract The total chromatic number χ ″ ( G ) of G is the smallest number of colors needed to color all elements of G in such a way that no adjacent or incident elements get the same color. The harmonic index H ( G ) of a graph G is defined as the sum of the weights 2 d ( u ) + d ( v ) of all edges uv of G, where d ( u ) denotes the degree of the vertex u in G. In this paper, we show a relation between the total chromatic number and the harmonic index. Also, we give relations between total chromatic number and some topological indices of a graph. More »» |

2015 |
J. Geetha and Dr. Somasundaram K., “Total coloring of generalized sierpiński graphs”, Australasian Journal of Combinatorics, vol. 63, no. 1, pp. 58-69, 2015.[Abstract] A total coloring of a graph is an assignment of colors to all the elements of the graph in such a way that no two adjacent or incident elements receive the same color. In this paper, we prove the tight bound of the Behzad and Vizing conjecture on total coloring for the generalized Sierpiński graphs of cycle graphs and hypercube graphs. We give a total coloring for the WK-recursive topology, which also gives the tight bound. © 2015,University of Queensland. All rights reserved. More »» |

2015 |
Aa Gupta, J. Geetha, and Dr. Somasundaram K., “Total coloring algorithm for graphs”, Applied Mathematical Sciences, vol. 9, pp. 1297-1302, 2015.[Abstract] A total coloring of a graph is an assignment of colors to all the elements of graph such that no two adjacent or incident elements receive the same color. Behzad and Vizing conjectured that for any graph G the following inequality holds: Δ(G)+1≤X′′(G)≤Δ(G)+2, where Δ(G) is the maximum degree of G. Total coloring algorithm is a NP-hard algorithm. In this paper, we give the total coloring algorithm for any graph and we discuss the complexity of the algorithm. © 2015 Aman Gupta, J. Geetha and K. Somasundaram. More »» |

Year of Publication | Title |
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2015 |
J. Geetha and Dr. Somasundaram K., “Total Coloring for Certain Classes of Claw-free Graphs”, in International Conference on Graph Theory and its Applications, Puducherry, 2015. |

Faculty Research Interest: